Analytical Solutions to Edge Effect of Composite Laminates Based on Symplectic Dual System

YAO Wei-an; NIE Yi-zhu; XIAO Feng

doi:10.3879/j.issn.1000-0887.2011.09.001

Volume 32 Issue 9

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YAO Wei-an, NIE Yi-zhu, XIAO Feng. Analytical Solutions to Edge Effect of Composite Laminates Based on Symplectic Dual System[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1021-1029. doi: 10.3879/j.issn.1000-0887.2011.09.001

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Analytical Solutions to Edge Effect of Composite Laminates Based on Symplectic Dual System

doi: 10.3879/j.issn.1000-0887.2011.09.001

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China;
Department of Computer Science, Dalian Medical University, Dalian, Liaoning 116044, P. R. China

Received Date: 2011-04-02
Rev Recd Date: 2011-07-01
Publish Date: 2011-09-15

Abstract

Abstract

In symplectic space composed of the original variables-displacements and their dual variables-stresses,the symplectic solution for the composite laminated based on the Pipes-Pagano model was established.In contrast to traditional technique,the symplectic dual variables include displacement components as well as stress components,so the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously.After introducing into the symplectic dual system,the uniform scheme,such as the separation of variables and symplectic eigenfunction expansion method,can be implemented conveniently to analyze problem of composite laminates.An analytical solution for free edge effect of composite laminates was gained,and it shows that the symplectic dual method is efficient for the analysis of composite laminates.
- composite laminates,
- edge effect,
- Pipes-Pagano model,
- interlaminar stresses,
- symplectic dual system

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References(12)

References

[1]	Pipes R B, Pagano N J. Interlaminar stresses in composite laminates under uniform axial extension[J]. J Comp Mater, 1970, 4(10): 538-548.
[2]	Pipes R B, Pagano N J. Interlaminar stresses in composite Laminates—an approximate elasticity solution[J]. J Appl Mech Trans ASME, 1974, 41(9): 668-672. doi: 10.1115/1.3423368
[3]	Hsu P W, Herakovick C T. Edge effects in angle-ply composite laminates[J]. J Comp Mater, 1977, 11(4): 422-438. doi: 10.1177/002199837701100405
[4]	Bar-Yoseph P, Pian T H H. Calculation of interlaminar stress concentration in composite laminates[J]. J Comp Mater, 1981, 15(5): 225-239. doi: 10.1177/002199838101500303
[5]	Tang S. A boundary layer theory—part Ⅰ: laminated composites in plane stress[J]. J Comp Mater, 1975, 9(1): 33-41. doi: 10.1177/002199837500900104
[6]	Wang S S, Choi I. Boundary-layer effects in composite laminates: part Ⅰ—free-edge stress singularities[J]. J Appl Mech Trans ASME, 1982, 49(9): 541-548. doi: 10.1115/1.3162514
[7]	Mittelstedt C, Becker W. Free-edge effects in composite laminates[J]. Applied Mechanics Reviews, 2007, 60(5): 217-245. doi: 10.1115/1.2777169
[8]	Timoshenko S P, Goodier J N. Theory of Elasticity[M]. 3rd ed. New York: McGraw-Hill, 1970.
[9]	钟万勰.弹性力学求解新体系[M].大连: 大连理工大学出版社, 1995.(ZHONG Wan-xie. A New Systematic Methodology for Theory of Elasticity[M]. Dalian: Dalian University of Technology Press, 1995.(in Chinese))
[10]	Zhong W X, Yao W A. The Saint Venant solutions of multi-layered composite plates[J]. Advances in Strunctural Engineering, 1997, 1(2): 127-133.
[11]	Yao W A, Yang H T. Hamiltonian system based Saint Venant solutions for multi-layered composite plane anisotropic plates[J]. I J Solids & Structures, 2001, 38(32): 5807-5817.
[12]	Yao W A, Zhong W X, Lim C W. Symplectic Elasticity[M]. Singapore: World Scientific, 2009.